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Expression of type Conditional

from the theory of proveit.logic.sets.functions.bijections

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional, f
from proveit.logic import And, Bijections, InSet, Injections, Surjections
In [2]:
# build up the expression from sub-expressions
expr = Conditional(And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B))), InSet(f, Bijections(A, B)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right) \land \left(f \in \left[A \xrightarrow[\text{onto}]{} B\right]\right) \textrm{ if } f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 10
operands: 5
3Literal
4ExprTuple6, 7
5ExprTuple14, 8
6Operationoperator: 10
operands: 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operands: 18
9ExprTuple14, 13
10Literal
11ExprTuple14, 15
12Literal
13Operationoperator: 16
operands: 18
14Variable
15Operationoperator: 17
operands: 18
16Literal
17Literal
18ExprTuple19, 20
19Variable
20Variable